Why would someone want to live in low income housing in a high income neighborhood? So that there is no bus so they have to spend all of their money on gas and then they have to blow what's left of their paycheck at Whole Foods instead of getting better value at Walmart or Family Dollar? So that they can pay inflated prices for everything? Pro tip (that's what the kids say now, right?): that burger that costs $14 at Sourced Hipster Local Organic Gluten Free Craft Crafty Craft Tap Room Gastropub With a Side of More Handcrafted Craft (with weekend run club, of course) isn't any different than the burger that is 5.99 at Joe's Eats.
Low income housing is also relative. Here in Huntington Beach, they have to build X number of units for lower end end rent. We have Wal-Mart, Target, Costco, lots of fast food, reasonable groery stores as well as Whole Paycheck. There are multiple 99 Cent Stores and a couple of Dollar Trees in HB.
A friend and I are going to one of our favorite places for a bite later on. It's a store front Mexican place. They make homemade chips and great, huge steak burritos that cost $6.99.
By the way Eat at Joe's is around the corner. Their very average burgers are about $9-10. Yes, there are expensive places and tourist traps, but there are a ton of reasonably prices places.
Just a few blocks from where I live is a small neighborhood of lower rent units. A little way from there is another such neighborhood. There's virtually no crime crime in either location. The kids from the lower income housing do well in school.
It can be done.